Let Σ be a smooth projective complex curve and g a simple Lie algebra of type ADE with associated adjoint group G. For a fixed pair (Σ, g), we construct a family of quasiprojective Calabi-Yau threefolds parameterized by the base of the Hitchin integrable system associated to (Σ, g). Our main result establishes an isomorphism between the Calabi-Yau integrable system, whose fibers are the interme...

makes a good alternative to the well-known Sine-Gordon equation as one more model of the two-dimensional integrable relativistic field theory with the self-action. In [3] the authors had suggested the construction of the finite-gap solutions for this equation. These are periodic and/or almost periodic function in x, t associated with special classes of double sheet ramified coverings of Riemann...

We prove that the ramified Prym map P g , r <mm...

1.1. QCoh on a stack. We know that QCoh forms a stack, i.e., sheaf of groupoids, over Schfpqc(S) for any scheme S. Thus if we have an fpqc sheaf of groupoids X over S, we can define QCoh(X ) as maps of sheaves X → QCoh on Schfpqc(S). By 2-Yoneda, this definition agrees with the usual notion of quasicoherent sheaves if X is a scheme. For various other (usually equivalent) definitions in the case...